CAN THEY DENY ME UNEMPLOYMENT BENEFITS JUST BECAUSE I AM GETTING SEVERANCE PAY?
No. Normally, pay that you receive after your termination date delays the commencement of your unemployment claim. Examples are accrued but unpaid vacation pay and sick pay. An exception to this rule is severance pay, but only if you have to sign a release of claims in order to get it (which is almost always the rule).
So, if you obtained severance or separation pay and had to sign a release of claims in order to get it, you may file for and obtain unemployment benefits for the same period. You do not need to wait until the severance period ends. Furthermore, you should file right away because if you wait, you will not be able to collect benefits dating back to the termination date.